I believe that we should start mathematics education with programming, then go to generator systems for numbers and operators over them, then how to form lattices and operators on patterns in the lattice, and do approximately continuous math and physics only at the very end.
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The very essence of the problem is the assumption that a space consists of infinitely many sizeless points. That idea goes back to Greeks, leads to Zeno paradoxes. Aristotle had a (finite) treatment to avoid those but it was reversed by Cantor and his colleagues. Hmm, no good.
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Aristotle is also underrated as a psychologist! What a guy!
End of conversation
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